تنزیل به تاخیر افتاده و پاداشهای احتمالی: فرآیندها و صفات

Discounting of delayed and probabilistic rewards was examined in two relatively large samples (Ns>100). For both types of rewards, a hyperbola-like discounting function provided good fits to individual data. Amount of reward had opposite effects on temporal and probability discounting: Smaller delayed rewards were discounted more steeply than larger delayed rewards, whereas larger probabilistic rewards were discounted more steeply than smaller probabilistic rewards. The nonlinear scaling parameter of the hyperbola-like function was larger for larger probabilistic rewards, but did not vary with the amount of delayed reward. Taken together, these findings suggest that despite the similar form of the temporal and probability discounting functions, separate processes may underlie the discounting of delayed and probabilistic rewards. Finally, weak to moderate positive correlations were observed between the discounting of delayed and probabilistic rewards. This finding is inconsistent with the notion of an “impulsiveness” trait that links an inability to delay gratification with a tendency to gamble and take risks.

Choices often involve outcomes that occur at different points in time and/or outcomes that are more or less likely to occur. Such choices have been studied under the rubrics intertemporal choice and risky choice, respectively. Intertemporal and risky choice represent traditional topics in microeconomics and are critical for understanding many aspects of decision-making, including consumer behavior (e.g., Becker, 1996; Kagel, Battalio, & Green, 1995; Loewenstein, 1988). In an analysis of purchases of home air conditioners, for example, Hausman (1979) addressed such issues as the tradeoffs between purchase price, durability, and energy efficiency. These tradeoffs pit the price paid now against the energy and replacement costs paid later, and exemplify questions frequently faced by consumers: “Should one spend more now on an item that will cost less to use and maintain in the future, or should one spend less now and risk having to pay more later?” In recent years, behavioral economics has substantially influenced the way researchers understand decision-making in situations involving such tradeoffs. By highlighting decision-making tendencies that represent anomalies from the perspective of standard economic theory, behavioral economists have demonstrated the limitations of an approach that assumes that humans are purely rational decision-makers (e.g., Prelec & Loewenstein, 1991; Thaler, 1991). Instead, behavioral economists have highlighted the role played by psychological factors in choice behavior (e.g., Green & Kagel, 1987; Loewenstein & Elster, 1992). Two areas in particular have received increasing attention in behavioral economics – temporal and probability discounting. Temporal discounting refers to the fact that the present, subjective value of a reward decreases as the delay until its receipt increases. Similarly, probability discounting refers to the fact that the subjective value of a reward decreases as the odds against receiving it increase (i.e., as the probability of its receipt decreases). These two types of discounting represent ways of thinking about the phenomena that fall under the larger rubrics of intertemporal and risky choice, respectively. In addition to the obvious parallel in the definitions of the two types of discounting, there are interesting parallels in the way they are manifested in certain kinds of situations. For example, Prelec and Loewenstein (1991) have noted that there are corresponding behavioral anomalies in intertemporal and risky choice. Moreover, similar mathematical functions can describe both the decrease in subjective value as delay increases and the decrease in subjective value as the odds against an outcome occurring increase. For example, Green, Myerson, and Ostaszewski (1999) showed that a function of the form equation(1) V=A/(1+bX)s describes both temporal and probability discounting. In Eq. (1), V represents subjective value, A represents the amount of reward, b is a parameter that (with s held constant) governs the rate of discounting, and s is a nonlinear scaling parameter. X represents the independent variable, either the time until or the odds against receiving a reward. For temporal discounting, according to Myerson and Green (1995), the parameter b is affected by the amount of delayed reward whereas s is not affected. In contrast, according to Loewenstein and Prelec (1992), s is inversely proportional to b. Thus, any variable (such as amount) that affects one parameter will also affect the other. For probability discounting, Green et al. (1999) again assumed (at least tacitly) that the parameter b is affected by the amount of reward but that s is not affected, whereas Prelec and Loewenstein (1991) assumed that s is directly proportional to b. Moreover, they proposed a different form for the probability discounting function, one similar to Eq. (1) except that X represents the logarithm of 1.0 plus the odds against receiving a reward. 1 One goal of the present study is to compare the probability discounting models proposed by Green et al. and by Prelec and Loewenstein. A related goal is to determine whether the s parameters of the temporal and probability discounting functions are independent of the amount of reward. 1.1. Underlying processes The various similarities between temporal and probability discounting raise the question as to the exact nature of the relationship between the two. More specifically, do these similarities arise because the same mechanism(s) underlie both types of discounting? For example, it has been proposed that these similarities exist because choices involving delayed rewards and choices involving probabilistic rewards both entail risk (e.g., Green & Myerson, 1996; Stevenson, 1986). That is, probabilistic rewards, by their very nature, are risky, with the degree of risk depending on the odds against actually receiving the reward. However, delayed rewards are also risky because with increasing delay, there is usually an increasing likelihood that something will occur to prevent an individual from receiving the reward. Alternatively, it has been proposed that similarities between temporal and probability discounting exist because both reflect the effect of delay on decision-making (e.g., Rachlin, Raineri, & Cross, 1991). The role of delay in temporal discounting is obvious, but as Rachlin et al. argued, probabilistic rewards may be thought of as repeated gambles in which the lower the probability, the more times, on average, the gamble has to be repeated before a win occurs. Thus, the lower the probability, the longer the wait will be before a reward is received. A third possible explanation for the similarities is that both temporal and probability discounting may reflect the same set of underlying principles. Prelec and Loewenstein (1991) have proposed that both types of reward discounting reflect two fundamental psychological properties of attribute weighting. First, there is what they term the “decreasing absolute sensitivity” of preference to an attribute of a reward. That is, increasing the attributes of two choice alternatives by a constant results in a decrease in the extent to which one is preferred to the other. For example, compare how strongly you prefer receiving $10 to receiving $1, on the one hand, with how strongly you prefer receiving $1000 to receiving $991. Second, there is what they term “increasing proportional sensitivity.” That is, multiplying the attributes of two alternatives by a constant increases the extent to which one is preferred to the other. For example, compare how strongly you prefer receiving $10 to receiving $1, on the one hand, with how strongly you prefer receiving $1000 to receiving $100. Prelec and Loewenstein (1991) argued that a hyperbola-like discounting function similar to Eq. (1) is consistent with these two principles when they are applied to the attributes of delay and probability as well as when they are applied to the attribute of amount. For example, consider the application of decreasing absolute sensitivity to the attribute of delay. Compare your preference for receiving $100 one day from now versus receiving $100 in one month with your preference for receiving $100 in 6 months plus one day versus receiving $100 in 7 months. Although the more immediate reward may be preferred in both cases, our sense is that preference will be stronger in the first case, and both published data (e.g., Green, Fristoe, & Myerson, 1994) and an informal survey of friends are consistent with this intuition. Despite the similarities between temporal and probability discounting with respect to both the mathematical form of the discounting function and the pattern of anomalies, recent research has revealed that there are a number of differences between the two. For example, some variables may affect one type of discounting but not the other. Ostaszewski, Green, and Myerson (1998) showed that high inflation rates affected the rate of discounting delayed rewards but not probabilistic rewards. Perhaps the most striking difference between temporal and probability discounting, however, concerns the effects of amount of reward on discounting rate. Specifically, larger delayed amounts are discounted less steeply than smaller delayed amounts, whereas the reverse is true for probabilistic reward amounts. That is, larger probabilistic amounts are discounted more steeply than smaller probabilistic amounts (Du, Green, & Myerson, 2002; Green et al., 1999; Prelec & Loewenstein, 1991). This finding represents a problem for a single-process account of discounting (i.e., one in which the same mechanism is assumed to underlie both temporal and probability discounting). After all, if the same mechanism were involved in discounting delayed and probabilistic rewards, then one would expect that the same variable (e.g., amount of reward) would have similar effects on both. Thus, some findings (e.g., the similar form of temporal and probability discounting functions) are consistent with a single-process account whereas other findings (e.g., opposite amount effects) are not. 1.2. Underlying traits Just as it is of interest whether a single process underlies both types of discounting, it is also of interest whether a single trait underlies both an individual’s tendency to discount delayed rewards and his or her tendency to discount probabilistic rewards. Moreover, these questions may be related. For example, according to one single-process account, both types of discounting are reducible to the effect of delay on subjective value. If this account were correct, and if individuals differed in their sensitivity to delay, then one would expect individuals’ temporal and probability discounting to show a strong positive correlation. Similarly, individuals’ temporal and probability discounting also should show a strong positive correlation if both types of discounting were reducible to the effect of risk, although a positive correlation might also arise because of the similarity of the assessment procedures (i.e., because of shared method variance, Campbell & Fiske, 1959). A strong negative correlation, however, would also be consistent with a single trait although it would imply that different processes underlie temporal and probability discounting. Consider the view that both types of discounting reflect “impulsiveness.” Impulsiveness may have a variety of different meanings (Barratt & Stanford, 1995), which generally include an inability to wait for delayed rewards (e.g., Ainslie, 1992) as well as a tendency toward risk-taking (Steel & Blaszczynski, 1998), or both (e.g., Richards, Zhang, Mitchell, & de Wit, 1999). For example, the standard definition of Attention-Deficit/Hyperactivity Disorder (Diagnostic and Statistical Manual, 4th ed.; American Psychiatric Association, 1994) includes impulsivity under the diagnostic criteria, where impulsivity is described as manifesting itself as impatience and as engaging in potentially dangerous behaviors without regard for the possible consequences. If impulsiveness underlies both impatience and risk-taking, then impulsive individuals would be expected to show steep discounting of delayed rewards (i.e., an inability to delay gratification) but shallow discounting of probabilistic rewards (i.e., a failure to take risk into account). Finally, if the two types of discounting reflect separate traits, then temporal and probability discounting should be relatively independent. That is, the extent to which individuals discount delayed rewards should tell us relatively little about their tendency to discount probabilistic rewards, and vice versa, as evidenced by an absence of correlation between these measures. 1.3. The present study Two quite different approaches were used in the present study to examine similarities and differences between temporal and probability discounting. The first approach examined whether an experimental manipulation (namely, varying the amount of reward) that affects the extent to which people discount rewards also affects the scaling parameter of the discounting function (i.e., s in Eq. (1)). Although Myerson and Green (1995) examined the empirical relationship between b and s in the temporal discounting function, the data they analyzed came from only 12 individuals, and the relationship between the parameters of the probability discounting function has never been experimentally evaluated. The second approach examined the correlation between temporal and probability discounting in order to determine the extent to which individuals’ behavior on one type of task predicts their behavior on the other type of task. The results of these individual-difference analyses may shed light on the issue of whether the two types of discounting reflect the same or different processes, as well as on the issue of whether a single trait underlies both temporal and probability discounting. These issues were addressed in two samples of participants using identical experimental designs but differing somewhat in the values of the independent variables that were studied with each sample.

The present findings have implications for the nature of the relationship between temporal and probability discounting. Our results are consistent with those of previous studies in showing that a hyperbola-like discounting function (Eq. (1)) accurately describes both temporal and probability discounting data. However, the present results also show that amount of reward has different effects on the exponent (s) of this function depending on whether the reward is delayed or probabilistic. Taken together with the opposite effects that amount of reward has on the degree to which delayed and probabilistic rewards are discounted, our findings suggest that, despite the similarity in the form of the discounting function, different mechanisms underlie temporal and probability discounting. The present results also provide little support for the hypothesis that a single trait of impulsivity underlies the discounting of both delayed and probabilistic rewards. The measures of temporal and probability discounting were positively (rather than negatively) correlated, and this result is inconsistent with a conception of impulsivity that links an inability to delay gratification (i.e., steep temporal discounting) with a tendency to gamble and take risks (i.e., shallow probability discounting).